# Numerical Mathematics and Scientific Computing

- Research Group -

**Head:**

Volker John

**Coworkers:**

Naveed Ahmed, Najib Alia, Felix Anker, Clemens Bartsch, Gabi Blättermann, Laura Blank, Jürgen Borchardt, Alfonso Caiazzo, Wolfgang Dreyer, Patricio Farrell, Jürgen Fuhrmann, Swetlana Giere, Lennard Kamenski, Alexander Linke, Christian Merdon, Jeanne Pellerin, Galina Printsypar, Gerd Reinhardt, Rainer Schlundt, Hang Si, Holger Stephan, Timo Streckenbach, Ulrich Wilbrandt

**Secretary:**

Marion Lawrenz

APPRENTICESHIP TRAINING: Mathematical-Technical Software Developer

**Apprentices:**Chiara D'Alonzo and Paul Söldner

Training Supervisor: Gerd Reinhardt

**Contact:**Phone: +49 30 20372 566, Fax: +49 30 20372 317

The mathematical modeling of a large number of scientific and technical problems leads to systems of differential equations describing the interactions of temporal and spatial variations of the considered physical processes. If the spatial variations are irrelevant, the processes are described by ordinary differential equations (ODEs). The connection with additional algebraic equations results in differential-algebraic equations (DAEs). DAEs are used to model, e.g., electrical networks and chemical plants. If the spatial structure of the process is important, partial differential equations (PDEs) are utilized as models. PDEs describe problems from structural analysis, from fluid mechanics, electro-magnetic problems, or particle diffusion. In general, it is not possible to solve the equations arising from applications in closed form. Numerical methods have to be used to obtain approximate solutions.

The research group develops, analyzes, and implements modern numerical methods for the solution of systems of PDEs and DAEs. An essential aspect of the studied methods is their practicability in applications.

The emphasis of the research activities is on:

- finite element and finite volume methods for the spatial discretization of PDEs,
- implicit schemes for their temporal discretization,
- numerical methods for systems of DAEs and resulting questions of numerical linear algebra and
- computational geometry (grid generation).

The research group takes part in the following main application areas: